Hoel et al., Introduction to Stochastic Processes

“Concise and very good for a one-semester course.” — Ebenezer George, University of Memphis

“I consider this text to be the best of its kind.” — O. Enchev, Boston University

“This book is well structured with topics that can be covered in one semester. I particularly like the topics chosen because they are not only of importance in theory, but also applicable to many areas such as economics, finance, engineering, and so on. The presentation is clear and reader friendly.” — Yimin Xiao, Michigan State University

“A classic book that looks better and better as time goes by.” — N. D. Singpurwalla, George Washington University

2. Stationary Distributions of a Markov Chain
Elementary properties of stationary distributions / Examples / Average number of visits to a recurrent state / Null recurrent and positive recurrent states / Existence and uniqueness of stationary disruptions / Queuing chain / Convergence to the stationary disruption / Proof of convergence

3. Markov Pure Jump Processes
Construction of jump processes / Birth and death processes / Properties of a Markov pure jump process

4. Second Order Processes
Mean and covariance functions / Gaussian processes / The Wiener process

5. Continuity, Integration, and Differentiation of Second Order Processes
Continuity assumptions / Integration / Differentiation / White noise

6. Stochastic Differential Equations, Estimation Theory, and Spectral Distributions
First order differential equations / Differential equations of order n / Estimation theory / Spectral distribution